The first thing to say about the contested cartoons published by a Danish paper last September is that some are, indeed, offensive. Jyllands-Posten took up the case of a Danish author who could find no one to illustrate a book about the prophet Muhammad. The paper, presenting this as a case of self-censorship, asked 12 illustrators for depictions of the prophet, and the one that has caused immense offence shows the prophet wearing a turban that conceals a fizzing bomb.

The cartoonist can't be accused of ignorance or lack of research - he has scrupulously transcribed a verse from the Qur'an on the turban - and there's no doubt that this is seriously offensive, and not just to Muslims but anyone who values truthful debate. It just isn't true to say that, from its founding, Islam would inevitably lead to suicide bombing, or even that its founder's teachings bear responsibility for this particular brand of atrocity.

That accusation, if made of any religion or secular school of thought that has spawned violent followers - a comparable image of Marx, say, or, quite plausibly, Darwin - would in most cases be just as offensive and wrong. In this case there is a special, deliberate offence to Muslims because the religion has an edict against such depictions.

Whether action should be taken, in a western democracy, against an argument that is just wrong, or against deliberate offence caused, however great, is another question. It's difficult to see that personal offence should be the basis of legal action in a state professing commitment to freedom of speech. The state takes a view on when personal offence is reasonable and when it threatens to infringe someone else's liberty, largely based on whether offence is caused generally, or just to a section of the community. Do the Danish cartoons cause offence only to isolated individuals? Or do they so attack anyone professing to be a Muslim that they would be caught by the UK's religious hatred law?

The cartoons almost certainly look very different to a Muslim living in a western democracy and to someone in the Muslim world. It's easy to sympathise with a Muslim living in Denmark, who would feel directly persecuted by these images. The Copenhagen Muslim interviewed in yesterday's Guardian certainly had a point when he compared them to the comments of a Danish MP who apparently called Muslims "a cancer in Denmark". Many people in his situation live difficult lives, and such images won't improve matters much.

But along with the sympathy one has to feel for people in that beleaguered situation, the uses that the Danish cartoons have been put to in the Muslim world must be challenged. Around the world, the anti-Danish campaign is being used by Islamist political groups to rally support for extreme causes. The aim of many such groups is, through pressure, to limit free speech on religious matters in the west, and entirely suppress it at home.

It is often forgotten to what degree law-making in the west is still seen across the globe as a model of good practice; and for that single reason our freedom of speech, even if exercised for the purposes of causing offence, even if simply wrong in practice, can't be eroded. To take an example: in Bangladesh in 1994, an attempt was made to introduce a law limiting what could be said on religious subjects. It failed because, it was argued, its terms could not be paralleled in the laws of any democracy. Britain's new law on religious hatred, even in its limited form, removes that defence from liberal voices outside Europe.

Debate on a great many subjects is already severely limited in the Muslim world. Reading Robert Irwin's brilliant new book, For Lust of Knowing: The Orientalists and their Enemies, it is a shock to learn that serious scholarly work by historians on the first years of Islam has to be expressed in code, lest it cause offence to the faithful by contradicting the received account. It is unlikely that a newspaper in a Muslim country will ever want to commission a cartoon along the Danish lines. But we are really talking about groups, even in relatively liberal Muslim countries, that want to draw the lines of permitted debate much tighter than they are at present.

In practice, our freedom of speech is not seriously threatened. Cartoonists will probably be careful about exercising good taste in such an area, as they already do on parallel subjects - for instance, in drawing an Israeli or Jewish politician, a cartoonist will probably avoid the hateful conventions of anti-semitic caricature. After the boycotts and a few noble-sounding words, we will probably go on much as before.

And that's probably the best thing to do. If anti-democratic forces in the Muslim world can make such effective use of a cartoon in a small European country, they would be much more encouraged by any signs of restriction on our part. Anyone in the Muslim world arguing for freedom of speech, on religious or other matters, has only one place to look to - the west. We ought to take into account the sorts of factions in the Muslim world who would regard legal restrictions on our side as part of a wider victory.

· Philip Hensher is the author of The Mulberry Empire comment@theguardian.com

Gary Younge: No

In January 2002 the New Statesman published a front page displaying a shimmering golden Star of David impaling a union flag, with the words "A kosher conspiracy?" The cover was widely and rightly condemned as anti-semitic. It's not difficult to see why. It played into vile stereotypes of money-grabbing Jewish cabals out to undermine the country they live in. Some put it down to a lapse of editorial judgment. But many saw it not as an aberration but part of a trend - one more broadside in an attack on Jews from the liberal left.

A group calling itself Action Against Anti-Semitism marched into the Statesman's offices, demanding a printed apology. One eventually followed. The then editor, Peter Wilby, later confessed that he had not appreciated "the historic sensitivities" of Britain's Jews. I do not remember talk of a clash of civilisations in which Jewish values were inconsistent with the western traditions of freedom of speech or democracy. Nor do I recall editors across Europe rushing to reprint the cover in solidarity.

Quite why the Muslim response to 12 cartoons printed by Jyllands-Posten last September should be treated differently is illuminating. There seems to be almost universal agreement that these cartoons are offensive. There should also be universal agreement that the paper has a right to publish them. When it comes to freedom of speech the liberal left should not sacrifice its values one inch to those who seek censorship on religious grounds, whether US evangelists, Irish Catholics or Danish Muslims.

But the right to freedom of speech equates to neither an obligation to offend nor a duty to be insensitive. There is no contradiction between supporting someone's right to do something and condemning them for doing it. If our commitment to free speech is important, our belief in anti-racism should be no less so. These cartoons spoke not to historic sensitivities, but modern ones. Muslims in Europe are now subjected to routine discrimination on suspicion that they are terrorists, and Denmark has some of Europe's most draconian immigration policies. These cartoons served only to compound such prejudice.

The right to offend must come with at least one consequent right and one subsequent responsibility. If newspapers have the right to offend then surely their targets have the right to be offended. Moreover, if you are bold enough to knowingly offend a community then you should be bold enough to withstand the consequences, so long as that community expresses displeasure within the law.

So far this has been the case. Despite isolated acts of violence that should be condemned, the overwhelming majority of the protests have been peaceful. Several Arab and Muslim nations have withdrawn their ambassadors from Denmark. There have been demonstrations outside embassies. Meanwhile, according to Denmark's consul in Dubai, a boycott of Danish products in the Gulf has cost the country $27m.

The Jyllands-Posten editor took four months to apologise. That was his decision. If he was not truly sorry then he shouldn't have done so; if he was then he should have done so sooner. Given that it took yet one more month for the situation to deteriorate to this level, these recent demonstrations can hardly be described as kneejerk.

"This is a far bigger story than just the question of 12 cartoons in a small Danish newspaper," Flemming Rose, the culture editor of Jyllands-Posten, told the New York Times. Too right, but it is not the story Rose thinks it is. Rose says: "This is about the question of integration and how compatible is the religion of Islam with a modern secular society - how much does an immigrant have to give up and how much does the receiving culture have to compromise."

Rose displays his ignorance of both modern secular society and the role of religion in it. Freedom of the press has never been sacrosanct in the west. Last year Ireland banned the film Boy Eats Girl because of graphic suicide scenes; Madonna's book Sex was unbanned there only in 2004. American schoolboards routinely ban the works of Alice Walker, JK Rowling and JD Salinger. Such measures should be opposed, but not in a manner that condemns all Catholics or Protestants for being inherently intolerant or incapable of understanding satire.

Even as this debate rages, David Irving sits in jail in Austria charged with Holocaust denial for a speech he made 17 years ago; the Muslim cleric Abu Hamza is on trial in London for inciting racial hatred; and a retrial has been ordered for the BNP leader, Nick Griffin, on the same charges. The question has never been whether you draw a line under what is and what is not acceptable, but where you draw it. Rose and others clearly believe Muslims, by virtue of their religion, exist on the wrong side of the line.

As a result they are vilified twice: once through the cartoon, and again for exercising their democratic right to protest. The inflammatory response to their protest reminds me of the quote from Steve Biko, the South African black nationalist: "Not only are whites kicking us; they are telling us how to react to being kicked."